" If "y=x^(x^(x).....oo)quad ," prove that "x(dy)/(dx)=(y^(2))/(1-y log x)

Similar Questions

Explore conceptually related problems

If y=x^(x^(x^(...oo))) , then prove that, (dy)/(dx)=(y^(2))/(x(1-y log x)) .

"If "y=a^(x^(a^(x...oo)))", prove that "(dy)/(dx)=(y^(2)(logy))/(x[1-y(logx)(logy)])

"If "y=a^(x^(a^(x...oo)))", prove that "(dy)/(dx)=(y^(2)(logy))/(x[1-y(logx)(logy)]).

Differentiate the following w.r.t.x. y = x^(x^(x^( oo))) , prove that x (dy)/(dx) = (y^2)/(1 - y log x)

If y=a^(x^(x^(2)*oo)), prove that (dy)/(dx)=(y^(2)log y)/(x(1-y log x*log y))

If y = x^y , prove that (dy)/(dx) = (y^2)/(x(1 - y log x))

If y = x^(x ^(x^(x ^(x.... oo) then prove that x dy/dx = y^2/(1- y logx )

If y=e^(x^(e ^(x^(...oo)))) ,show that, (dy)/(dx)=(y^(2)logy)/(x(1-y log x logy)) .

If y=(sqrt(x))^((sqrt(x))^((sqrt(x))^(...oo) , show that, x (dy)/(dx)=(y^(2))/(2-y log x).